Ch 2 – The Normal Distribution YMS – 2.1

1. Ch 2 – The Normal DistributionYMS – 2.1 Density Curves and the Normal Distributions

2. Vocabulary • Mathematical Model • An idealized description of a distribution • Density Curve • Is always on or above the horizontal axis • Has area = 1 underneath it • Can roughly locate the mean, median and quartiles, but not standard deviation • Mean is “balance” point while median is “equal areas” point.

3. Reminder: Exploring Data on a Single Quantitative Variable • Always plot your data • Identify socs • Calculate a numerical summary to briefly describe center and spread • Describe overall shape with a smooth curve • Label any outliers

4. Greek Notation • Population mean is μ and population standard deviation is σ • These are for idealized distributions (population vs. sample) Classwork p83 #2.1 to 2.5 Next 2 classes – Fathom Activity and Sketching WS

5. Activity: Beauty and the GeekMore Vocabulary • Normal Curves • Are symmetric, single-peaked and bell-shaped • They describe normal distributions • Inflection point • Point where change of curvature takes place • Could use this to estimate standard deviation

6. 3 Reasons for UsingNormal Distributions 1. They are good descriptions for some distributions of real data. 2. They are good approximations to the results of many kinds of chance outcomes. 3. Many statistical inference procedures based on normal distributions work well for other roughly symmetric distributions.

7. The 68-95-99.7 Rule • In N(μ, σ), rule gives percent of data that falls within 1, 2, and 3 standard deviations, respectively. • AKA Empirical Rule Classwork p89 #2.6-2.9 Homework p90 #2.12, 2.14, 2.18 and 2.2 Reading Blueprint

8. Sketch a bell curve for each of the following: • p(x < a ) = 0.5 • p(x > b) = 0.5 • p(x < c) = 0.8 • p(x < d) = 0.2 • p(x > e) = 0.05 • p(x > f) = .95

9. YMS – 2.2 Standard Normal Calculations

10. Standards • Standard Normal Distribution • N(0, 1) • Standardized value of x (z-score) • Data point minus mean divided by standard deviation • Gives you the number of standard deviations the data point is from the mean

11. Table A • Left Column has ones.tenths digit • Top Row has 0.0hundreths digit • LEFT COLUMN + TOP ROW = Z-SCORE • Area is always to the LEFT of the z-score

12. TI-83 Plus • Keystrokes • 2nd • DISTR • 1: normalpdf • Finds height of density curve at designated point • We won’t be using this • 2: normalcdf(lower limit, upper limit, mean, st. dev.) • Gives area under the curve to left or right of a point • 3:invNorm(area, mean, standard deviation) *When you don’t enter a mean or standard deviation, it assumes it is the Normal Distribution (0, 1)

13. In Class Exercisesp95 #2.19-2.20Homeworkp103 #2.21-2.25

14. Activity: Grading Curves WSNormal Probability Plots (NPP) • Is a plot of z-scores vs. data values • Use the calculator! • If it’s a straight line, the data is normally distributed. • How else do we assess normality?

15. In Class Exercises(Next 3 days)Shape of Distributions WSp108 #2.27p113 #2.41-2.42, 2.46-2.47,2.51-2.52, 2.54 AP Practice Packet